I doubt you would be interested in the area of NoData, so for the most part I would avoid calculating it. I also want to point out that rows*columns*area of the cell, does not return 'surface area' in the way we use that term. That formula is giving you the 2d area of the extent. Surface area can be calculated in ArcGIS though using Add Surface Information or Surface Volume tools. Zonal Geometry can be used to get 2d area of each zone in a dataset. It sounds like you want the area of the 'real' pixels though, so you can multiply any raster by 0 and Int it, like I showed you and then put it into this tool. Because it is a constant of 0, it would be considered 1 zone. Technically, you could just convert the raster of 0 to polygon and get area that way. I don't anticipate enhancing the Get Raster Properties tool in a way that would distinguish NoData pixels from valid pixels in terms of returning a count. There are other methods for that. We can consider returning total pixels based on col/row counts.
